Question

In: Math

When using Gaussian elimination to solve a system of linear equations, how can you recognize that...

When using Gaussian elimination to solve a system of linear equations, how can you recognize that the system has no solution?

Solutions

Expert Solution

Summary:

In these type of situations we try to find the reduced echelon format of the augmented matrix and check, if it has any row which has all the entries except last entry as zero and last entry is a numerical constant. In such cases we can easily say that the system of linear equations has no solution or the system of linear equations is inconsistent.


Related Solutions

in parts a and b use gaussian elimination to solve the system of linear equations. show...
in parts a and b use gaussian elimination to solve the system of linear equations. show all algebraic steps. a. x1 + x2 + x3 = 2 x1 - x3 = -2 2x2 + x3 = -1 b. x1 + x2 + x3 = 3 3x1 + 4x2 + 2x3 = 4 4x1 + 5x2 + 3x3 = 7 2x1 + 3x2 + x3 = 1
Write a MATLAB function function = pivGauss(.....) to solve linear equations using Gaussian Elimination with Partial...
Write a MATLAB function function = pivGauss(.....) to solve linear equations using Gaussian Elimination with Partial Pivoting. You'll need to employ Nested Loops. Thank you !
Solve the following system of equations using Gaussian or​ Gauss-Jordan elimination. w + x + y...
Solve the following system of equations using Gaussian or​ Gauss-Jordan elimination. w + x + y + z = -2 2w +2x - 2y - 2z = -12 3w - 2x + 2y + z = 4 w - x + 7y + 3z = 4
1. Solve linear system using Gaussian elimination a) x1 + 2x2 + x3 = 2 -x1...
1. Solve linear system using Gaussian elimination a) x1 + 2x2 + x3 = 2 -x1 − 3x2 + 2x3 = -3   x1 − 6x2 + 3x3 = -6 b) -2b + 2c = 10 3a + 12b -3c = -6 6a + 18b + 0c = 19 c) 4x - 1y + 4z + 3t = 5 1x - 4z + 6t = 7 5x - 5y + 1z + 2t = -5 4x + 1y + 3z +...
1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no...
1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) 3y + 2z = 1 2x − y − 3z = 4 2x + 2y − z = 5 (x, y, z) = 2) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION....
Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no...
Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, z, and w in terms of the parameters t and s.) 4x + 12y − 7z − 20w = 20 3x + 9y − 5z − 28w = 36 (x, y, z, w) = ( ) *Last person who solved this got it wrong
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 2y + z...
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 2y + z = 3 x + z = 2 4y − 3z = 13 solve for x,y,x
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y - 2z...
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y - 2z = 8 3x - 2y + 2z = 2 4x - y + 3z = 2 (x, y, z) = ?
1) Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 4y −...
1) Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 4y − 6z = 56 x + 2y + 3z = −2 3x − 4y + 4z = −21 (x, y, z) = 2) Solve the system of linear equations using the Gauss-Jordan elimination method. 5x + 3y = 9 −2x + y = −8 (x, y) =
For the following exercises, solve each system by Gaussian elimination.
For the following exercises, solve each system by Gaussian elimination.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT